Wednesday, February 6, 2013

A Multitude of Products

We have so far assumed that our man has the choice only between rest and producing a single product, apples. In our example he was prepared to work five hours to produce fifty apples.
We now take a small step away from the simplest model of economic life toward the enormous complexity of the actual economy by assuming that he can produce and consume more than one product. In order to simplify the presentation, however, we shall assume that our individual has only the alternative of producing and consuming one more product, pears. So far it was a choice between rest and work; now there is the additional choice between the production and consumption of several goods. In analyzing the basic principles of this choice we are faced with one of the most important problems in economics—namely the problem of how mankind allocates available resources to various possible productions.
In our example our producer worked five hours to achieve a total production of fifty apples. Let us suppose that he wants to work neither more nor less than before. To what extent will he replace the production and consumption of apples with those of pears, now that he has the choice between the two? The answer depends on the one hand upon his valuation of the relative utilities of pears and apples, and on the other hand upon the relative production costs of apples and pears. The question arises whether more or less time is needed to produce pears rather than apples.
When the choice is between work and rest, the utility of the products of work is, as we have seen, valued exactly according to the law of diminishing marginal utility: the utility of additional apples appears less as their number increases. The same law governs the decisions relating to the consumption of two products, apples and pears. Our man will, therefore, value pears lower in relation to apples, as soon as the quantity of the former increases. This also because the utility of apples now appears greater to him. For if we assume that our producer wishes to produce pears only by sacrificing some of the time hitherto employed in the production of apples, the latter become scarcer.
Our man might, for instance, consider the utility of the first 5 pears as equivalent to that of 15 apples (1 pear = 3 apples); the utility of the next 5 pears as equivalent to that of 10 apples (1 pear = 2 apples); and the utility of the next 5 pears as equivalent to that of 5 apples (1 pear = l apple). The next 5 pears might drop in his valuation to less than 5 apples.
These valuations are, of course, the result of the psychological fact that the appetite for pears decreases with increasing satisfaction, whereas the appetite for apples increases with decreasing satisfaction. We are assuming that the individuals are aware of this fact when making their production plans for a certain time period.
Anyone who is prepared to forgo apples if he can produce pears instead, demands from himself, as it were, pears in exchange for apples. The valuation of pears in relation to apples can, therefore, be represented by a demand curve in the usual way. On the assumption just mentioned, this curve will have the shape pictured in Figure 2.
It has become usual in recent years to present the distribution of a given income (or effort) between two consumption (or production) possibilities with the help of so-called indifference curves. Since this technique is generally less accessible to laymen than simple demand and supply curves, we have tried to do without it, especially as we believe that the introduction of the indifference curve technique does not involve any substantial change or progress. The method of presentation adopted here reaches essentially the same results.
Now how many pears will actually be produced, and how many apples sacrificed? This obviously depends upon the supply of pears. Pears are, so to speak, supplied by nature when work previously devoted to the production of apples is transferred to the production of pears. The supply of pears in terms of apples is, therefore, dependent upon the relative production costs of apples and pears—in other words upon how much more or less time it takes to produce pears rather than apples.
Our graph with its several supply curves shows how many apples and pears our man will produce, provided the assumptions underlying the demand curve remain unchanged.

FIG. 2
If we assume that it takes the same time to produce pears and apples, the horizontal supply curve is situated at the price of one apple, or curve S1. If it takes three times as much time to produce a pear as it does to produce an apple, the horizontal supply curve will run at the price of three apples, or curve S2. If to produce pears takes one-third of the time that it takes to produce apples, the supply curve will run at the price of one-third of an apple per pear, or curve S3. The position of the intersection points between the demand curve and the three supply curves immediately provides the answer to the question of how many pears and apples will be produced on our various assumptions. In the first case (represented by S1), our man produces 20 pears and sacrifices 20 apples in order to do so. Instead of having 50 apples he will now have 30 apples. In the second case (represented by curve S2), 10 pears are produced at a sacrifice of 30 apples. Instead of 50 apples there will now be 20 apples. In the third case (represented by curve S3), where only one-third of an apple need be sacrificed for the production of each pear, 23 pears will be produced at a sacrifice of nearly 8 apples. Instead of the original 50 apples there will now be 42.